In a conventional signal processing technology field, when a signal is sampled with two times a maximum signal frequency or larger based on a Shannon-Nyquist sampling theory, a signal component may be accurately reconstructed, and accordingly, two times the maximum signal frequency or larger is always used for a sampling frequency. However, it is currently identified that an original signal component can be reconstructed without incurring any loss through a new theory of compressive sensing even though a sampling frequency equal to or smaller than two times the maximum signal frequency is used.
The compressive sensing theory is based on sparsity of the signal. When any signal is observed by a random domain, most of the signal components become 0, and a few of the signal components have non-zero components. The signal is called a sparse signal. At this time, the number of signal components with non-zero values corresponds to sparsity.
For example, most components of a sinusoidal signal continuous on a time axis have non-zero values. However, when viewed from a frequency axis, the signal has the non-zero value only in a particular frequency, and most of the remaining frequency components have values of 0. The compressive sensing theory mainly says that the sparse signal may be reconstructed with only slight linear measurement without incurring loss of an original signal.
When an input sparse signal for performing the compressive sensing is x, a length of the sparse signal x is N, and sparsity of the sparse signal x, that is, the number of non-zero components in a particular domain is K, a linear measurement equation is defined in Equation (1).y=Ax  (1)
Here, A denotes a matrix having a size of M×N, wherein M has a value smaller than N and a length of a result value y of the linear measurement becomes M. Here, M/N is a compression rate of the signal, and efficiency of the compressive sensing increases when M is reduced to a minimum value possible. Meanwhile, a condition for reconstructing an original signal x by using a compressed signal y in the compressive sensing is generally defined as shown in Equation (2) for M, N, and sparsity K.M>O(K log(N/K))  (2)
Accordingly, in the compressive sensing, in order to reconstruct the original signal x from the compressed data y without any loss, a value of M should satisfy equation (2). Simultaneously, in order to achieve a maximum of compression efficiency, the value of M should be set to a minimum value, so that the value of M should be a minimum value satisfying Equation (2) to normally reconstruct the signal and improve the compression efficiency for compressive sensing.
Meanwhile, since sparsity information of the input signal x cannot be known in a conventional compressive sensing method, the compressive sensing is generally performed using a fixed A matrix. FIG. 1 illustrates an example of a signal compression process of the conventional compressive sensing method. Referring to FIG. 1, the input signal x transferred from a signal input unit 10 is converted to the output signal y through an operation with the A matrix by a signal compressor 20, and transferred to a signal processor 30. In the conventional method, the A matrix is fixedly predefined regardless of the sparsity of the input signal x, and a fixed value of M cannot satisfy Equation (2), so that it is failed to normally reconstruct the signal or compression efficiency of the signal is reduced since an unnecessarily large value of M is used.